DiceDesign: Designs of Computer Experiments

Package `DiceDesign'

October 12, 2022

Type Package Title Designs of Computer Experiments Version 1.9 Date 2021-02-10 Author Jessica Franco, Delphine Dupuy, Olivier Roustant,

Patrice Kiener, Guillaume Damblin and Bertrand Iooss. Maintainer Celine Helbert Description Space-Filling Designs and space-filling criteria (distance-based and uniformity-

based), with emphasis to computer experiments; . License GPL-3 Depends R (>= 2.10) Suggests rgl, randtoolbox, lattice Encoding latin1

URL NeedsCompilation yes LazyData true Repository CRAN Date/Publication 2021-02-13 00:10:11 UTC

R topics documented:

DiceDesign-package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 discrepancyCriteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 discrepESE_LHS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 discrepSA_LHS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 dmaxDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 factDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 faureprimeDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 lhsDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

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DiceDesign-package

maximinESE_LHS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 maximinSA_LHS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 meshRatio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 mindist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 mstCriteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 nolhDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 NOLHdesigns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 nolhdrDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 NOLHDRdesigns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 OA131 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 OA131_scrambled . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 olhDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 phiP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 rss2d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 rss3d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 runif.faure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 scaleDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 straussDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 unif.test.quantile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 unif.test.statistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 unscaleDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 wspDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 xDRDN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Index

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DiceDesign-package Designs of Computer Experiments

Description Space-Filling Designs (SFD) and space-filling criteria (distance-based and uniformity-based).

Details This package provides tools to create some specific Space-Filling Design (SFD) and to test their quality:

? Latin Hypercube designs (randomized or centered) ? Strauss SFD and Maximum entropy SFD, WSP designs ? Optimal (low-discrepancy and maximin) Latin Hypercube desigsn by simulated annealing and

genetic algorithms, ? Orthogonal and Nearly Orthogonal Latin Hypercube designs, ? Discrepancies criteria, distance measures, ? Minimal spanning tree criteria, ? Radial scanning statistic

DiceDesign-package

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Note

Part of this work was conducted on 2006-2009 within the frame of the DICE (Deep Inside Computer Experiments) Consortium between ARMINES, Renault, EDF, IRSN, ONERA and TOTAL S.A. ().

In this package, only Faure's sequence is implemented. Note that the randtoolbox package provides the following quasi random sequences: the Sobol sequence, the Halton (hence Van Der Corput) sequence and the Torus sequence (also known as Kronecker sequence). Note also that the lhs package provides other types of algorithms to compute optimized LHS.

Author(s)

J. Franco, D. Dupuy, O. Roustant, P. Kiener, G. Damblin and B. Iooss. Thanks to A. Jourdan for discussions about OA131. Maintainer: Celine Helbert

References

Cioppa T.M., Lucas T.W. (2007). Efficient nearly orthogonal and space-filling Latin hypercubes. Technometrics 49, 45-55.

Damblin G., Couplet M., and Iooss B. (2013). Numerical studies of space filling designs: optimization of Latin Hypercube Samples and subprojection properties, Journal of Simulation, 7:276-289, 2013.

De Rainville F.-M., Gagne C., Teytaud O., Laurendeau D. (2012). Evolutionary optimization of low-discrepancy sequences. ACM Transactions on Modeling and Computer Simulation (TOMACS), 22(2), 9.

Dupuy D., Helbert C., Franco J. (2015), DiceDesign and DiceEval: Two R-Packages for Design and Analysis of Computer Experiments, Journal of Statistical Software, 65(11), 1?38.

Fang K.-T., Li R. and Sudjianto A. (2006) Design and Modeling for Computer Experiments, Chapman & Hall.

Fang K-T., Liu M-Q., Qin H. and Zhou Y-D. (2018) Theory and application of uniform experimental designs. Springer.

Nguyen N.K. (2008) A new class of orthogonal Latinhypercubes, Statistics and Applications, Volume 6, issues 1 and 2, pp.119-123. Owen A.B. (2020), On dropping the first Sobol point, .

Roustant O., Franco J., Carraro L., Jourdan A. (2010), A radial scanning statistic for selecting space-filling designs in computer experiments, MODA-9 proceedings.

Santner T.J., Williams B.J. and Notz W.I. (2003) The Design and Analysis of Computer Experiments, Springer, 121-161.

Examples

# ********************** # Designs of experiments # **********************

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coverage

# A maximum entropy design with 20 points in [0,1]^2 p ................
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